Abstract This lesson serves as the introduction
to a set of lessons related to the horrific nuclear
power plant disaster at Chernobyl in the Ukraine, part
of the former Soviet Union. Students will review the
process of unit analysis to convert between units of
radioactivity and will examine the radiation released
during the 10 days the fire at the power plant raged.

Objectives Students
will be able to:

i. Apply unit analysis to convert between Curies
(Ci) and Becquerels (Bq), which are units of radiation
used
to express the amount of radiation released.
ii. Use half-life data of radioactive nuclide
material to demonstrate the use of an exponential
function, specifically
calculating the amount of material remaining
after a given period of time.
iii. Covert from units of radiation curies
or becquerels to units of mass to determine
the scale of radioactive
material release during the Chernobyl disaster.

Math StandardsMeasurement
• Use unit analysis to check measurement computations.
• Make decisions about units and scales that are appropriate
for problem situations involving measurement.Connections
• Recognize and apply mathematics in contexts outside of
mathematics.

Teacher
BackgroundOn
April 26, 1986, due to a combination of the construction
of the power plant and human error, there was a melt down
inside the reactor in Unit #4 of the Chernobyl Nuclear
Power Plant. The subsequent steam explosion and fire blew
the 1000-ton roof off the building and allowed radioactive
material to escape. How much radiation were those workers
in direct proximity exposed to? At the time of the explosion
at Chernobyl, one source says that “on the roof of
the destroyed reactor building, radiation levels reached
a frightening 100,000 R per hour! “
(Source: http://www.agls.uidaho.edu/etoxweb/resources/Case%20Study/Chernob6.pdf)

The
total release of radionuclides to the environment
has been approximated to be somewhere in the range
of 1900 PBq of activity (in a Report to the US
Department of Energy) and 12 EBq (in the assessment
of the OECD Nuclear Power Agency). That is a range
of about 51 million Ci to 324 million Ci
(Source: http://agls.uidaho.edu/etoxweb/resources/Case%20Study/Chernob6.pdf)

1. Begin by telling your students the following story: On
4/28/86 at the Forsmark Nuclear Power Plant, which is 60
miles north of Stockholm, Sweden, suddenly signs of abnormally
high levels of radiation were found. Up to five times the
normal amount of radioactive emissions were found in the
soil and greenery around the plant. Even further north in
Sweden and Finland, where rain and snow were falling, the
same disquieting signals were discovered. The original fear
was that the Forsmark Plant was leaking radiation somehow.
After extensive searches, the scientists decided that the
plant was not losing radiation. It had to be coming from
somewhere else!

Examining the wind patterns for those days, the wind had
come up from the Black Sea, across the Ukraine, across the
Baltic Sea and into Scandinavia. In other words, something
terrible had happened in the Soviet Union, and the Soviet
officials were not telling anybody about it. That disaster
was Chernobyl.

2. Ask your students if they have ever heard of Chernobyl.
Since most of them were not born when the Chernobyl disaster
occurred, nearly 20 years ago in 1986, do not expect them
to know much, if anything, about Chernobyl.

3. Next ask your students where in the world they think Chernobyl
is located, considering how the winds carrying the radiation
had swept across the Ukraine. Put up Radiation Plume #1 overhead
(Source: http://agls.uidaho.edu/etoxweb/resources/Case%20Study/Chernob6.pdf figure #5) and mark the approximate location of Stockholm
to show how far the wind had carried the radiation in just
two days.

4. Share with the students the following:
On April 26, 1986, due to a combination of the construction
of the power plant and human error, there was a melt
down inside the reactor in Unit #4. The subsequent
steam explosion
and fire blew the 1000-ton roof off the building
and allowed radioactive material to escape.

5. If possible,
show the video, “Nowhere to Hide:
A Look at Chernobyl”
(source: http://www.ucg-terrehaute.org/video/chernobylbb.rm)
This 10-minute video gives a good picture of just how terrible
Chernobyl was and some of the health problems caused by the
radioactive materials released during this event. (Talking
with an individual who lived in Kiev at the time of the accident,
she says that the Geiger counters were recalibrated because
they had been used in a different experiment and not by governmental
decree)

If you
can’t
get the video, put up Chernobyl at the Time of Accident overhead
(Source: http://www.agls.uidaho.edu/etoxweb/resources/Case%20Study/Chernob6.pdf figure
#4) to show the damage to the reactor building and the huge
hole through which radiation escaped. Firefighters
battled the blaze, unaware of the terrible radiation, but
it continued for ten days.

6. Before you can talk about how much radiation
these workers and firemen were exposed to, you need
to talk about the various ways of measuring radiation.
Put up the Units of Radiation overhead and tell the
students that radiation has several different units
of measurement (see Teacher Background for further
information).

a. The roentgen (R) is a unit of radiation exposure
in air.

b. The rad (roentgen-absorbed-dose) is a unit
of absorbed radiation or a unit of dose. A
roentgen in air can be approximated by 0.87
rad in air, 0.93 rad in tissue, and 0.97 rad
in bone. Doses are commonly expressed in rads/hr
or mrads/hr or R/hr and mR/hr.

c. The rem (roentgen-equivalent-man) is a
unit of dose equivalent. The rem is the absorbed
dose in rads corrected for the equivalent absorption
in living tissue. The rem is equal to the rad
multiplied by a weighting factor depending
upon the type of radiation.

d. For x-rays, the weighting factor is one.
Therefore, for x-rays, one rem is equal to
one rad.

7. Tell student that they will now calculate approximately
how many mrems of radiation they are exposed to each
year. Using the Ionizing Radiation Exposure in the
United States guide sheet and the Calculating Your
Personal Radiation Exposure sheet (Source: http://www.ocrwm.doe.gov/pm/program_docs/curriculum/unit_2_toc/47.pdf
), have students calculate approximately how many
mrem they were exposed to this year. The average
per capita US dose is 360 mrem per year. Tell the
students that you can not assume a direct relationship
between rads and rems for all radiation, but for
x-rays it is a weighting factor of one. If they use
this factor for their total exposure, how many roentgens
where they exposed to?

8. Share with the students that at
the time of the explosion at Chernobyl, one source
says that “on
the roof of the destroyed reactor building, radiation
levels reached a frightening 100,000 R per hour! “
(Source: http://www.agls.uidaho.edu/etoxweb/resources/Case%20Study/Chernob6.pdf , page 2)
Students will use a ratio to calculate the factor
that their personal exposure must be multiplied by
to reach the level of exposure of the workers on
the roof after the exposure. Point out that while
their (the students’) exposure is over a year,
the exposure of the fireman and other workers was
per hour.

9. Share with the students that one
of the areas of controversy about Chernobyl is
the “source
term” which refers to how much radioactivity
was released from the exploded and burning reactor.
Before we can approximate the amount of radioactivity
released, we first need to deal with the units used
for measuring the gross radioactivity in a substance
that does not relate to doses or biological damage.
These units are the Curie (Ci) and the Becquerel
(Bq). These units both measure the rate at which
radioactive material decays in disintegrations per
sec (dps)

A curie, named after Madam Marie Curie, is the
amount of radioactivity in one gram of radium.
One gram of radium has 37,000,000,000 disintegrations
per second (3.7x10^10 dps). This means that one
curie of a different radioactive substance is
the amount of that material that will have 3.7x10^10
dps. Thus, one curie of plutonium is a different
number of grams from one curie of cesium.

A becquerel is the quantity of a radioactive
substance that will have one disintegration
per second (1 dps). One Ci =3.7x10^10 Bq.

In an
atomic reactor there are many billions curies of radioactivity.
The number four reactor at Chernobyl
was believed to have 9 billion curies of radioactivity.
To convert a large number of curies into becquerels,
we need much larger units of becquerels, like petabecquerels
(PBq) = 10^15 Bq or exabecquerels (Ebq )= 10^18 Bq.

10. Put up the Estimates of Amount of Radiation
Released at Chernobyl overhead, showing each estimate
separately. Ask students what they notice about these
estimates and why they might vary so significantly
depending upon the source.

a. 50 million curies of radioactive substances
plus another 50 million curies of rare and noble
gases was released (Russians and the International
Atomic Energy Agency (IAEA), 1986 report)

b. 30% of the nuclear core, 3 billion curies
of an estimated 9 billion curies was released
(The US Argonne National Laboratory, 1986)

c. 50% of the core’s radioactivity,
4.5 billion curies, was released (The US
Lawrence Livermore National Laboratory, 1986)

d. No less than 80 % of the reactor’s
radioactivity, which amounted to 6.4 billion
curies, was released. (Vladimir Chernousenko,
chief scientific supervisor of the “clean
up” for a 10-kilometer zone around the
exploded reactor, 1991)

e. At the Union of Concerned Scientists
Senior Energy analyst Kennedy Maize concluded
that
the “core vaporized – all 190 tons
of fuel and all 9 billion curies.”

As
the Chairman of the Chernobyl Committee in
Belarus said to Itar-Tass in Minsk on April
29, 1999, “No one knows how much fuel
was left there (at Chernobyl)”

11. Tell the students they are now
going to use unit analysis to convert from curies
to PBqs and from
PBq’s to Curies, given that and One Ci =3.7x10^10
Bq. Ask students how they would convert 50 million
curies (Ci) into PBqs. To do this they need to draw
upon the information about the relationship between
Ci & Bqs, as well as the relationship between
Bqs & PBqs. This exercise asks students to develop
a unit analysis equation and be able to use scientific
notation. (Teacher cheat sheet follows)

12.
Then ask the students how they would convert 85 PBqs
into Ci.

Teacher
cheat sheet: Use the following conversion ratios
to make it easier for you to check the students’ calculations
when converting from Ci’s to PBq’s or
from PBq’s to Ci’s:

Homework

1. Convert the
estimated amounts of total radiation released at Chernobyl
from Ci’s to PBq’s. (Answers are
given below amount)

a) 3 billion Ci

b) 4.5 billion Ci

c) 6.4 billion Ci

d) 9 billion Ci

2. Convert the
following estimated amounts of individual radioactive elements
released at Chernobyl from Pbq’s
into Ci’s (Answers are given below question. (You will
need these numbers for a later homework assignment)

a) 1600 – 1920
PBq”s

Lower estimate:

Upper
estimate:

b)
56 – 112
PBq’s

Lower
estimate:

Upper
estimate:

c)
8 – 12
PBq

Lower
estimate:

Upper
estimate:

d) 0.03
PBq

e) 0.042
PBq

Day 2

1. Ask the students if they think all of the radiation inside
the reactor was released. Students will have to draw upon
their understanding of radiation from science in answering
this question.

2. Share with the students the fact that radiation is apparently
leaking from the sarcophagus
built around the destroyed reactor. Ask the students “What
does this imply?” Hopefully they will realize that
there is still radiation inside.

4. Notice that the estimated maximum release of these twenty
important radionuclides totals a staggering 12,536 PBq. Ask
the students to calculate how many times larger this number
is than the original Soviet announcement of 50 million curies
being released. (12,536 PBq is approximately 340 million
curies, which is nearly 6.5 times the original Soviet estimate.)

For an
analysis of the accident’s consequences, the
most significant of the radionuclides released are radioactive
Iodine (),
radioactive Caesium (),
and radioactive Strontium ().
Radioactive Plutonium ()
and its various decay products, some which have a half-life
of 24,000 years, causes concern
about long-term contamination.

Hopefully all of the students have heard of the half-life
of a radioactive substance. It is the amount of time it takes
for one half of the original amount of a radioactive substance
to decay.

But before we can use the half-life to determine how long
the radioactive material will be radioactive, we need to
calculate the number of grams of the material was originally
released.
To do this we must first calculate the specific activity
(SpA) of the particular radionuclide in units of disintegrations
per unit time/ unit mass. The SpA is calculated from the
basic formula:where

If the students
have done some chemistry, they should be able to derive
the formula for SpA by using unit analysis
and Avogadro’s number. If they don’t have the
experience in chemistry, simply substitute the numbers into
the formula to get:

or

This equation is satisfactory when the half-life
of the nuclide is expressed in seconds. If however, the half-life
is expressed in other units, such as days, then a separate
time conversion is required. Have students use time conversion
factors to arrive at the following equation:

***
Teacher cheat notes: Here are other formulas for the SpA
of a radioactive element depending whether the
half-life is in minutes, hours, or years. I’d recommend
using just one formula so the students will become familiar
with that particular formula.

1.

2.

3.

Source: U.S. Department
of Health, Education, and Welfare: Radiological Health
Handbook:
January 1970.

5. Looking at the SpA formula for a radioactive
element whose half life is measured in days, ask students
to think about how the specific activity of the radionuclide
with a half life of 8 days ()
compares to the specific activity of the radionuclide with
a half life of 30 years ()?

Teacher Cheat Sheet: To calculate the SpA of , which has
a half-life of 8.0 days.

To Calculate the SpA of , which has a half-life of 30 years,

The students should notice that the radionuclide with the
shorter half-life has a greater value of specific activity,
SpA , than the SpA of the radionuclide with the longer half-life.
This means that the shorter the half-life of a radionuclide,
the more Curies given off per gram of the nuclide, and the
more Curies given off per gram means the radionuclide decays
faster.

Activity
2: Part 1: Simply by looking at the length of the
half-life of each of the following radionuclides, arrange
them in order from the radionuclide with the lowest SpA value
to the radionuclide with the highest Spa value

1) (Half-life:30
yrs) 2) (Half-life:28
yrs)

3) (Half-life:24,400
yrs) 4) (Half-life:6,580
yrs)

Answer: , , ,

Part
2: Use the SpA formula for a half-life given in years,

to determine the SpA for each of the following radioactive
elements.

1) (Half-life:30
yrs) answer:

2) (Half-life:28
yrs) answer:

3) (Half-life:24,400
yrs) answer:

4) (Half-life:6,580
yrs) answer:

6.
Ask the students how to determine the range of the number
of grams of released
at Chernobyl. (To do this, divide the estimated amount
of Ci’s released, calculated in last
night’s homework, by the SpA of )

Lower estimate: =

Upper estimate: =

An estimated
range for the amount of released
is

Activity
3: Use the specific values of the SpA to calculate
the number of grams of each of the following radionuclides
released during the Chernobyl disaster. (These estimates
will be used in the homework of this lesson)

1) 56 – 112
PBq’s

Lower
estimate: =

Upper
estimate: =

2) 8 – 12
PBq’s

Lower estimate: =

Upper estimate: =

3) 0.03
PBq

=

4) 0.042
PBq

=

Now that we know approximately how much of each radionuclide
was released, we can calculate how long the radiation from
that nuclide will remain in the environment, if it were all
deposited in one location. To calculate the amount of time,
we start with radiation decay equation:

where

But we want to know the time, t, it takes for the radionuclide
to decay completely. The equation needs to be rewritten into
the form (If the students are familiar with natural logarithms
have them convert the half life equations to allow them to
solve for the time t otherwise give them the formula):

Now
do the calculation for .
Remember that since the natural logarithm of zero does
not exist, this
means .
Instead a small number like grams.

Lower estimate of 348.7 grams:

Upper estimate of 418.5 grams:

Remember,
these numbers are based upon estimations, and are meant
to give approximate values. The “actual “reported
values might be different.

Homework:

Have the students
use the modified radiation decay equation to determine
how long it will take for each of the following
radionuclides to decay “completely” if the total
amount were deposited in one place. (Since you cannot use
, choose a small value like grams)

1) 56 – 112
PBq (half-life: 30 years)

2) 8 – 12
PBq (half-life: 28 years)

3) 0.03
PBq (half-life: 24,400 years)

4) 0.042
PBq (half-life: 6,580 years)

Please
make sure that you tell your students that the radiation
was scattered
and did not settle in just one location. However,
there are still many “hot spots” where the radiation
is too high for people to live.

Closure
By calculating the amount of radiation released and calculating
an “approximate” length of time it will take
for the radioactive materials to decay completely, the students
should begin to realize the seriousness of the Chernobyl
disaster.

Embedded
Assessment

Students should be assessed throughout the lesson on their ability to use unit
analysis to grasp the amount of radiation released upon the world by this single
incident. The discussion that should follow the homework needs to deal with the
health issues that are still occurring now and will continue to occur in the
future.

PULSE
is a project of the Community Outreach and Education
Program of the Southwest Environmental Health Sciences
Center and is funded by: